What is the integral of [arcsin(x)]^2 ?

The integral of [arcsin(x)]^2 is xarcsin^2(x)-2(-arcsin(x)sqrt(1-x^2)+x)+C

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integral of [arcsin(x)]^2

\int [arcsin (x)]^{2} d x

x arcsin^{2} (x) - 2 (- arcsin (x) 1 - x^{2} + x) + C

Solution steps

\int [arcsin (x)]^{2} d x

Simplify

= \int arcsin^{2} (x) d x

Apply Integration By Parts

: x arcsin^{2} (x) - \int \frac{2 x arcsin ( x )}{1 - x ^{2}} d x

= x arcsin^{2} (x) - \int \frac{2 x arcsin ( x )}{1 - x ^{2}} d x

\int \frac{2 x arcsin ( x )}{1 - x ^{2}} d x = 2 (- arcsin (x) 1 - x^{2} + x)

= x arcsin^{2} (x) - 2 (- arcsin (x) 1 - x^{2} + x)

Add a constant to the solution

= x arcsin^{2} (x) - 2 (- arcsin (x) 1 - x^{2} + x) + C

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What is the integral of [arcsin(x)]^2 ?
The integral of [arcsin(x)]^2 is xarcsin^2(x)-2(-arcsin(x)sqrt(1-x^2)+x)+C